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Some variants of the method of fundamental solutions: regularization using radial and nearly radial basis functions

Csaba Gáspár (2013)

Open Mathematics

The method of fundamental solutions and some versions applied to mixed boundary value problems are considered. Several strategies are outlined to avoid the problems due to the singularity of the fundamental solutions: the use of higher order fundamental solutions, and the use of nearly fundamental solutions and special fundamental solutions concentrated on lines instead of points. The errors of the approximations as well as the problem of ill-conditioned matrices are illustrated via numerical examples....

Spectres et groupes cristallographiques. II : domaines sphériques

Pierre Bérard, Gérard Besson (1980)

Annales de l'institut Fourier

Dans cet article, nous donnons une description des spectres du laplacien dans certains domaines sphériques. Les représentations des groupes de Coxeter cristallographiques y jouent un rôle fondamental.

Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions

David Krejčiřík (2014)

Mathematica Bohemica

We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the hypersurfaces tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the area of the Neumann...

Stability results for Harnack inequalities

Alexander Grigor'yan, Laurent Saloff-Coste (2005)

Annales de l’institut Fourier

We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically...

Stationary solutions of two-dimensional heterogeneous energy models with multiple species

Annegret Glitzky, Rolf Hünlich (2004)

Banach Center Publications

We investigate stationary energy models in heterostructures consisting of continuity equations for all involved species, of a Poisson equation for the electrostatic potential and of an energy balance equation. The resulting strongly coupled system of elliptic differential equations has to be supplemented by mixed boundary conditions. If the boundary data are compatible with thermodynamic equilibrium then there exists a unique steady state. We prove that in a suitable neighbourhood of such a thermodynamic...

Su alcune questioni connesse con il problema di derivata obliqua regolare per le funzioni armoniche

Enrico Magenes (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

— Vengono riconsiderati il problema di derivata obliqua regolare e quello misto di Dirichlet-derivata obliqua regolare per le funzioni armoniche in un dominio di R 3 e le questioni di completezza hilbertiana connesse già studiate in un precedente lavoro e viene data una nuova dimostrazione di un teorema di unicità.

Superconvergence by Steklov averaging in the finite element method

Karel Kolman (2005)

Applicationes Mathematicae

The Steklov postprocessing operator for the linear finite element method is studied. Superconvergence of order 𝓞(h²) is proved for a class of second order differential equations with zero Dirichlet boundary conditions for arbitrary space dimensions. Relations to other postprocessing and averaging schemes are discussed.

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